廬
NOISE ANALYSIS OF FET TRANSIMPEDANCE AMPLIFIERS
The availability of detailed noise spectral density character-
istics for the OPA111 amplifier allows an accurate noise
error analysis in a variety of different circuit configurations.
The fact that the spectral characteristics are guaranteed
maximums allows absolute noise errors to be truly bounded.
Other FET amplifiers normally use simpler specifications of
rms noise in a given bandwidth (typically 10Hz to 10kHz)
and peak-to-peak noise (typically specified in the band
0.1Hz to 10Hz). These specifications do not contain enough
information to allow accurate analysis of noise behavior in
any but the simplest of circuit configurations.
Noise in the OPA111 can be modeled as shown in Figure 1.
This model is the same form as the DC model for offset
voltage (E
OS
) and bias currents (I
B
). In fact, if the voltage
e
n
(t) and currents i
n
(t) are thought of as general instantaneous
error sources, then they could represent either noise or DC
offsets. The error equations for the general instantaneous
model are shown in Figure 2.
where N rms is the rms value of some random variable n(t).
In the case of amplifier noise, n(t) represents either e
n
(t) or
i
n
(t).
R
2
R
1
e
n
(t)
e
n
(t)
V
I
n鈥?/div>
(t)
e
n
(t)
R
3
I
n+
(t)
e
O
(t) = e
n
(t) [1 + R
2
/R
1
] + I
n鈥?/div>
(t) R
2
+ I
n+
(t) R
3
[1 + R
2
/R
1
]
FIGURE 2. Circuit With Error Sources.
The internal noise sources in operational amplifiers are
normally uncorrelated. That is, they are randomly related to
each other in time and there is no systematic phase relation-
ship. Uncorrelated noise quantities are combined as root-
sum-squares. Thus, if n
1
(t), n
2
(t), and n
3
(t) are uncorrelated
then their combined value is
N
TOTAL
rms
=
N
12
rms
+
N
2 2
rms
+
N
3 2
rms
(2)
e
n
(t)
鈥?/div>
I
n鈥?/div>
(t)
V
Noiseless Amplifier
+
I
n+
(t)
Amplifier With Noise
The basic approach in noise error calculations then is to
identify the noise sources, segment them into conveniently
handled groups (in terms of the shape of their noise spectral
densities), compute the rms value of each group, and then
combine them by root-sum-squares to get the total noise.
TYPICAL APPLICATION
The circuit in Figure 3 is a common application of a low
noise FET amplifier. It will be used to demonstrate the
above noise calculation method.
R
2
I
IN
位
CR1
e
O
e
O
= I
IN
R
2
FIGURE 1. Noise Model of OPA111.
If the instantaneous terms represent DC errors (i.e., offset
voltage and bias currents) the equation is a useful tool to
compute actual errors. It is not, however, useful in the same
direct
way to computer noise errors. The basic problem is
that noise cannot be predicted as a function of time. It is a
random variable and must be described in probabilistic
terms. It is normally described by some type of average鈥?/div>
most commonly the rms value.
鈭?/div>
T
N rms
=
1 / T
鈭?/div>
Q
n
2
(t) dt
漏
(1)
FIGURE 3. Pin Photo Diode Application.
1994 Burr-Brown Corporation
AB-076
1
Printed in U.S.A. February, 1994
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